Chapter 10
Rachel Botic Hr. 7
10.1- areas of parallelograms and trapezoids
Vocabulary:
*Base of a Parallelogram: is the length of any one of it's sides
*Height of a Parallelogram: the perpendicular distance between the base and the opposite side
*Bases of a Trapezoid: are it's two parallel sides
*Height of a Trapezoid: the perpendicular distance between the bases
How to solve for Areas of Parallelograms
A=bh-----------------Write out formula first
A=5x3----------------Then fill in the numbers that are the base and height
A=15 units2-------Multiply to give you your answer
**LABELS!!**
How to solve for Areas of Trapezoids
A=1/2(b1+b2)h--------Write out formula first
A=1/2(4+8)3------------Fill in correct numbers from the trapezoid
A=18 units2-----------Multiply to give you your answer
**LABELS!!**
real life example
10.2- Areas of Circles
Vocabulary:
*Area: the amount of surface the figure covers
*Circle: is the set of all points in a plane that are the same distance from a fixed point in the center
*Radius: the distance from the center to any point on the circle
*Diameter: is the distance across the circle that crosses through the center of the circle
*Circumference: the distance around the circle
*Pi: the non-repeating decimal that we use for finding the circumference and area of a circle
video on how to find the circumference of a circle
How to find the area of a circle
A= TTr2--------------Write out formula first
A=3.14(5)2----------Fill in the radius to solve,**remember to use 3.14 if told to**
A=78.5 units2-----Multiply to get your answer,**remember to round correctly if told to** **LABELS!!!**
real life example for circumference
10.3 three-dimensional figures
*solid: a three dimensional figure that encloses a part of space
*polyhedron: a solid that is enclosed by polygons
*face: the polygons that form a polyhedron
*prism: is a polyhedron, that has two congruent bases that are parallel to each other.
*pyramid: is a polyhedron, that has one base, and the other faces are triangles
*cylinder: is NOT a polyhedron, and is a solid with two bases that are parallel to each other.
*cone: is a solid with one circular base
*sphere: is a solid formed by all points in space that are the same distance from a fixed point called the center.
*edge: the segments where faces of a polyhedron meet
*vertex: is a point where three or more edges meet.
Example of a Prism
Example of a Pyramid
Example of a Cylinder
Example of a Cone
example of a sphere
10.4 surface areas of prisms and cylinders
Vocabulary:
*net: a two-dimensional pattern that forms a solid when it is folded
*surface area: is the sum of the area of it's faces.
how to find the surface area of a prism
S=2B+Ph-----------------------------------Write out formula first
S=2(1/2x10x12)+(13+13+10)15----Then fill in the numbers to solve
S=660 units2----------------------------Multiply
**Labels!!**
**For a triangular prism remember to multiply by 1/2!**
How to find the surface area of a cylinder
S=2TTr2+2TTrh--------------Write out formula first
S=2TT(4)2+2TT(4)(10.7)---Fill in numbers to solve
S=369.45 units2------------Multiply
**Labels!!**
Real life example to use surface area
10.5 surface areas of pyramids and cones
Vocabulary:
*slant height: or l of a regular pyramid is the height of a lateral face, which is, any face that isn't the base
video on how to find the surface area of a pyramid
how to find the surface area of a cone
S=TTr2+TTrl-----------------Write out the formula first
S=TT(4)2+TT(4)(9)---------Fill in the numbers to solve
S=163.4 units2-------------Multiply
**LABLES!!**
real life example to use surface area
10.6 Volumes of Prisms and cylinders
Vocabulary:
*volume: is a measure of a solid's amount of space it takes up
finding volumes of prisms
V=lwh----------------Write out formula first
V=12(8)(2)----------Fill in numbers to solve
V=192 units3-----Multiply
**LABELS!!**
** remember if a triangular pyramid divide by 1/2**
finding volumes of cylinders
V=TTr2h--------------Write out formula first
V=TT(3)2(9)----------Fill in numbers to solve
V=81 units3--------Multiply
**LABELS!!**
real life example for using volume
10.7 volumes of pyramids and cones
Vocabulary:
*pyramid: is a polyhedron, that has one base as any polyhedron, with the other faces as triangles
*cones: a solid with one circular base
*volume: is a measure of a solid and how much space it takes up
video on how to find the volume of a pyramid
finding the volume of a cone
V=1/3TTr2h----------------Write out formula first
V=1/3TT(6)2(12)----------Fill in numbers to solve
V=452.389 units3-------Multiply
**LABELS!!**
real life example for using volume
All formulas in chapter 10
10.1 formulas
Area of a Parallelogram: A=bh
Area of a Trapezoid: A=1/2(b1+b2)h
10.2 formulas
Area of a Circle: A=TTr2
Circumference: C=TTd or C=2TTr
10.4 formulas
Surface Area of a Prism: S=2B+Ph Triangular: S=1/2(2)B+Ph
Surface Area of a Cylinder: S=2B+Ch OR S=2TTr2+ 2TTrh
10.5 formulas
Surface Area of a Pyramid: S=B+1/2Pl "B"=area of the base-lw
Surface Area of a Cone: S=TTr2+TTrl
10.6 formulas
Volume of a Rectangular Prism: V=Bh "B"=area of the base-lw
Volume of a Triangular Prism: V=Bh "B"=area of the base-1/2lw
Volume of a Cylinder: V=Bh "B"=area of the base-TTr2
10.7 formulas
Volume of a Pyramid: V=1/3Bh "B"=area of the base-lw
Volume of a Cone: V=1/3Bh "B"=area of the base-TTr2
Volume of a Sphere: V=4/3TTr3
Surface Area of a Sphere: A=4TTr2